一类非线性发展方程弱解的长时间性态(英文)  

LARGE TIME BEHAVIOR FOR THE WEAK SOLUTION OF THE NONLINEAR EVOLUTION EQUATION

作　　者：董柏青[1] 高永东[2] 秦晓红[1] 吴娥子[1] 

机构地区：[1]华中科技大学数学系,湖北武汉430074 [2]咸宁学院数学系,湖北咸宁437005

出　　处：《数学杂志》2004年第5期479-484,共6页Journal of Mathematics

基　　金：SupportedbyNaturalScienceFoundationofChina(1 0 0 0 1 0 1 3) ;KeyItemofXianningCollege(KL0 31 6)

摘　　要：本文分别在全空间和半空间两种情形下讨论一类非线性发展方程弱解的长时间性态 ,证明了其弱解在L2 范数下衰减速率和线性热方程一致 ,分别为t-n2 (1r-12 ) 和t-n2 (1r-12 ) -12 .In this paper the authors study the large time behavior for the weak solution of the nonlinear evolution equation in the whole space and the half space and prove that the solution decays in L^2 norm at t~~^(-n2(1r-12)) and t~~^(-n2(1r-12)-12),respectively, which is the same as the solution of the heat equation.

关 键 词：长时间性态 非线性发展方程 

分 类 号：O175.29[理学—数学] O177.92[理学—基础数学]